One feature to be noticed is that from Fig. REF  and Fig. REF , there exist both time “delay” and “advance” events, i.e., some neutrino events are found to be
later than the GRB photons whereas some neutrino events are found to be earlier than the photons. One possibility is that the associations of neutrino
events with GRBs are purely accidental. However, it is suggested in ref. [1]} that the IceCube Neutrino Observatory can not distinguish between neutrinos and anti-neutrinos, therefore the co-existence of both time “delay” and “advance” events can be explained by the different propagation properties between neutrinos and anti-neutrinos. The different propagation properties between neutrinos and anti-neutrinos can be explained by the \(CPT\) -odd feature of the linear Lorentz violation [2]}, indicating an asymmetry between neutrinos and anti-neutrinos.
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